Showing papers by "Robert E. Tarjan published in 1976"
TL;DR: An algorithm is presented which finds a maximum independent set in an n-vertex graph in 0($2^{n/3}$) time and can thus handle graphs roughly three times as large as could be analyzed using a naive algorithm.
Abstract: We present an algorithm which finds a maximum independent set in an n-vertex graph in 0($2^{n/3}$) time. The algorithm can thus handle graphs roughly three times as large as could be analyzed using a naive algorithm.
489 citations
TL;DR: This paper studies methods for finding minimum spanning trees in graphs and results include relationships with other problems which might lead general lower bound for the complexity of the minimum spanning tree problem.
Abstract: This paper studies methods for finding minimum spanning trees in graphs. Results include 1. several algorithms with $O(m\log \log n)$ worst-case running times, where n is the number vertices and m is the number of edges in the problem graph; 2. an $O(m)$ worst-case algorithm for dense graphs (those for which m is $\Omega (n^{1 + \varepsilon } )$ for some positive constant $\varepsilon $); 3. an $O(n)$ worst-case algorithm for planar graphs; 4. relationships with other problems which might lead general lower bound for the complexity of the minimum spanning tree problem.
427 citations
TL;DR: This paper provides a linear-time algorithm for computing an st-numbering for any biconnected graph and can be combined with some new results by Booth and Lueker to provide alinear-time implementation of the Lempel-Even-Cederbaum planarity-testing algorithm.
294 citations
TL;DR: An algorithm for finding two edge-disjoint spanning trees rooted at a fixed vertex of a directed graph using depthfirst search and an efficient method for computing disjoint set unions is presented.
Abstract: This paper presents an algorithm for finding two edge-disjoint spanning trees rooted at a fixed vertex of a directed graph. The algorithm uses depthfirst search and an efficient method for computing disjoint set unions. It requires O (e?(e, n)) time and O(e) space to analyze a graph with n vertices and e edges, where ? (e, n) is a very slowly growing function related to a functional inverse of Ackermann's function.
179 citations
TL;DR: It is shown that for each graph withn vertices and maximum in-degreed, there is a pebbling strategy which requires at mostc(d) n/logn pebbles, and this bound is tight to within a constant factor.
Abstract: We study a one-person game played by placing pebbles, according to certain rules, on the vertices of a directed graph. In [3] it was shown that for each graph withn vertices and maximum in-degreed, there is a pebbling strategy which requires at mostc(d) n/logn pebbles. Here we show that this bound is tight to within a constant factor. We also analyze a variety of pebbling algorithms, including one which achieves the 0(n/logn) bound.
176 citations
TL;DR: It is shown that determining who wins such a game if each player plays perfectly is very hard; this result suggests that the theory of combinational games is difficult.
Abstract: This paper considers a generalization, called the Shannon switching game on vertices, of a familiar board game called Hex. It is shown that determining who wins such a game if each player plays perfectly is very hard; in fact, if this game problem is solvable in polynomial time, then any problem solvable in polynomial space is solvable in polynomial time. This result suggests that the theory of combinational games is difficult.
159 citations
TL;DR: It is shown that for every k ≥ 3, the problem of determining whether an intersection graph of straight line-segments is k -colorable is NP -complete.
149 citations
03 May 1976
TL;DR: It is shown that for each graph with n vertices and maximum in-degree d, there is a pebbling strategy which requires at most c(d) n/log n pebbles, and this bound is tight to within a constant factor.
Abstract: We study a one-person game played by placing pebbles, according to certain rules, on the vertices of a directed graph. In [3] it was shown that for each graph with n vertices and maximum in-degree d , there is a pebbling strategy which requires at most c(d) n/log n pebbles. Here we show that this bound is tight to within a constant factor. We also analyze a variety of pebbling algorithms, including one which achieves the 0(n/log n) bound.
49 citations
TL;DR: This class of examples shows that an algorithm given in [STAN-CS-75-512] for computing functions defined on paths in trees is optimum to within a constant factor.
Abstract: Let $F_1$, $F_2$,..., $F_m$ be a set of Boolean functions of the form $F_i$ = $\wedge$ {x$\in X_i$}, where $\wedge$ denotes conjunction and each $X_i$ is a subset of a set X of n Boolean variables. We study the size of monotone Boolean networks for computing such sets of functions. We exhibit anomalous sets of conujunctions whose smallest monotone networks contain disjunctions. We show that if |$F_i$| is sufficiently small for all i, such anomalies cannot happen. We exhibit sets of m conjunctions in n unknowns which require $c_2$m$\alpha$(m,n) binary conjunctions, where $\alpha$(m,n) is a very slowly growing function related to a functional inverse of Ackermann''s function. This class of examples shows that an algorithm given in [STAN-CS-75-512] for computing functions defined on paths in trees is optimum to within a constant factor.
34 citations
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TL;DR: This work develops linear-time algorithms to find maximum weighted and unweighted degree-constrained subgraphs (b-matchings) of a tree and uses a generalization of an algorithm for finding a maximum 2-matching in a tree.
Abstract: We develop linear-time algorithms to find maximum weighted and unweighted degree-constrained subgraphs (b-matchings) of a tree. We use a generalization of an algorithm for finding a maximum 2-matching in a tree.
21 citations
01 Mar 1976
TL;DR: A hierarchy of global flow problem classes, each solvable by an appropriate generalization of the "node listing" method of Kennedy, are defined, and it is shown that each of these generalized methods is optimum, among all iterative algorithms, for solving problems within its class.
Abstract: This paper studies iterative methods for the global flow analsis of computer programs. We define a hierarchy of global flow problem classes, each solvable by an appropriate generalization of the "node listing" method of Kennedy. We show that each of these generalized methods is optimum, among all iterative algorithms, for solving problems within its class. We give lower bounds on the time required by iterative algorithms for each of the problem classes.
TL;DR: It is shown that for infinitely many n, there is a (non-reducible) flow graph H with n nodes (all with in-degree and out-degree bounded by two), such that any weak node sequence for H has length at least cn 2, where c is a positive constant.